arXiv:2312.01386v2 Announce Type: replace Abstract: Gaussian process upper confidence bound (GP-UCB) is widely used for sequential optimization of expensive black-box functions. Although many upper bounds on its cumulative regret have been established in the literature, whether GP-UCB is minimax optimal remains open. We study this question through the effective optimism level, defined as the product of the exploration coefficient and the regularization parameter in kernel ridge regression. Under a uniform confidence assumption, we prove a new regret lower bound for GP-UCB with Mat\'ern kernels
This research provides a theoretical update on a widely used algorithm in machine learning, showing its suboptimality under specific conditions, which is a continuous area of academic inquiry. It represents an incremental refinement in the understanding of algorithmic limitations.
For researchers and practitioners in sequential optimization, understanding the theoretical limits and suboptimality of GP-UCB influences algorithm selection and development. It highlights the ongoing need for more robust or minimax-optimal solutions in crucial AI applications.
This research re-calibrates the theoretical understanding of GP-UCB's efficiency, suggesting a need to reconsider its assumed optimality in certain contexts. It does not immediately change practical applications but informs future algorithmic improvements.
- · Machine Learning Researchers
- · Optimization Algorithm Developers
- · Practitioners over-relying on GP-UCB's assumed optimality
Increased academic focus on developing minimax optimal sequential optimization algorithms.
Potential for new algorithms to emerge that outperform GP-UCB in specific, theoretically defined scenarios.
Long-term, this could lead to more efficient and reliable black-box optimization in areas like hyperparameter tuning or scientific discovery.
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Read at arXiv cs.LG